Question: The grades on a chemistry midterm at Santa Rita are normally distributed with $\mu = 72$ and $\sigma = 5.5$. Ashley earned a n $81$ on the exam. Find the z-score for Ashley's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ashley's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{81 - {72}}{{5.5}}} $ ${ z \approx 1.64}$ The z-score is $1.64$. In other words, Ashley's score was $1.64$ standard deviations above the mean.